Question

What will be an annuity's price today if it will pay $2,000 at each year-end over the next 5 years? The annual interest rate is 8%.

a) $8,624.25
b) $10,000
c) $14,693.28
d) $2,938.60
e) None of the above

Answer 1

To find the present value of an annuity, the formula PV = Pmt * [(1 - (1 + r)^-n) / r] is used. Applying this with a $2,000 payment, 5 years, and an 8% interest rate, the present value is approximately $7,985. The correct answer is 'e) None of the above'.

Step-by-step explanation:

The question is asking to calculate the present value of an annuity that pays $2,000 at the end of each year for 5 years, given an annual interest rate of 8%. The present value of an annuity can be calculated using the present value of annuity formula: PV = Pmt * [(1 - (1 + r)^-n) / r], where Pmt is the annuity payment, r is the interest rate per period, and n is the number of periods.

Substituting the values into the formula:

PV = $2,000 * [(1 - (1 + 0.08)^-5) / 0.08]

PV = $2,000 * [(1 - (1.08)^-5) / 0.08]

PV = $2,000 * [(1 - 0.6806) / 0.08]

PV = $2,000 * [0.3194 / 0.08]

PV = $2,000 * 3.9925

PV = $7,985

Therefore, the price of the annuity today is approximately $7,985, which means the correct answer is 'e) None of the above'.